Sports economics books seem to be plentiful these days. The 2007 season brought two new monographs: Diamond Dollars: The Economics of Winning in Baseball by Vince Gennaro and The Baseball Economist: The Real Game Exposed by J.C. Bradbury. Each attempts to tackle a distinct area within the grasp of economic analysis.

Diamond Dollars is the more ambitious of the two. Gennaro assays nothing less than an uncovering of the mysteries of the baseball economy and purports to offer a model for small market teams to be successful. Gennaro covers a wide range of issues, from the relationship between winning and revenues, to the value of players, the dynamics of player development, a strategy for assembling a winning team and building a team brand.

Along the way, Gennaro reveals a basic understanding of the economics of baseball and, although not a formally-trained economist himself, a reasonable understanding of rudimentary microeconomic analysis. He addresses many disparate topics, but his core concept is the “win curve.” While there is nothing particularly novel here, Gennaro’s presentation puts a different spin on the marginal revenue of winning. Basically, he argues that the relevant range of wins per season is between 70 and 105. Below 70 or above 105 wins, he asserts, there is no relationship between winning and revenues. Within the range, there is a sweet spot between 86 and 91 wins that is the threshold for making it to the postseason, and, consequently, it is within this sweet spot that there is the highest incremental return to winning. Making it to the playoffs, according to Gennaro, has its biggest impact by increasing a team’s revenues in succeeding years. For teams below 70 wins, Gennaro’s thesis is that winning a few extra games brings them essentially no new revenue, meaning they have little incentive to spend on free agents, whether or not they receive transfers from the wealthy teams.

So far, so good. But here Gennaro hits a brick wall. His text suggests that he has subjected his theory to rigorous modeling and testing, yet he provides the reader with next to no information on how he has executed his empirical analysis. The few bits of explanation he does provide fail to inspire confidence.

For instance, Gennaro apparently has done some regression analysis where revenue is the dependent variable and team wins in the current and previous years are two of the arguments. We are not informed what the other independent variables are, nor are we told whether the relationship is tested linearly, nor for what years it is tested. Curiously, Gennaro does state that he has weighted the current and lagged team wins equally and that he has run a regression separately for each team to capture its distinct win curve. It is not clear how many years of data he has in each team regression or why he did not instead use team dummies and interactive variables in a pooled regression to identify these effects.

Furthermore, Gennaro estimates his revenue data. Here he makes some reasonable assumptions, but he also misses his target on some sources of revenue. Despite these problems, Gennaro intrepidly forges ahead, glibly making specific claims about various teams’ win curves. Unfortunately, most of the rest of Diamond Dollars suffers from similar weaknesses.

Detailed problems appear throughout the book. Here is a small sample of these difficulties. Gennaro does not adequately source his discussion. The few footnotes and citations he does provide often confuse or obfuscate the matter. He claims that he has developed a model to evaluate players’ productivity, but he neither explains the model nor does he cite the pioneering work of Gerald Scully in this field or its lineage. Later in the book, Gennaro appears to assert authorship of the idea that baseball’s revenue sharing would be more effective if it were based on the value of a team’s market, rather than on a team’s revenue. Yet this position has been amply discussed in the professional and journalistic literature. Indeed, it is even incorporated into MLB’s latest collective bargaining agreement, which Gennaro entirely misses.

Gennaro also makes inaccurate claims about financial data. For example, he states that the NFL “generates over $2.5 billion in annual broadcast revenues” and that “about 80 percent of the NFL’s $5 billion in revenue is shared” (p. 4). The correct numbers would be over $3.5 billion, about 70 percent, and over $6 billion. On the next page, he writes that “$40 million from MLB’s central fund” is distributed equally to each team annually. The actual number in the last two years has been under $30 million. Such errors are not catastrophic, except when one tries to make detailed claims about a team’s revenue or a player’s value.

Gennaro devotes an entire chapter to teams’ player development systems. Here too there are broad generalizations and data inaccuracies that mar his discussion. He estimates that an average team devotes $12 million yearly to its player development system (scouting, signing bonuses, operation of minor league affiliates.) The actual average is almost 50 percent higher. In a footnote, however, Gennaro states that his estimate excludes international scouting and bonuses, perhaps accounting for the lower number. Yet, it is curious why he would exclude the international aspect of player development, when today almost half of all minor leaguers come from outside the continental United States.

One of the book’s concluding chapters is entitled “A Strategic Approach to Assembling the Roster.” Here Gennaro uses his hidden statistical method to find that the ratio of player productivity to player salary reveals that per dollar of output pitchers cost 14 percent more than position players and that left-handed pitchers cost 17 percent more. The inference is that team general managers should be particularly cautious in overpaying for these positions. The important question that Gennaro does not address is that if his estimates are correct, why doesn’t the market correct itself over time? And if the market does correct itself, what is left of his policy recommendations? The unstartling punch line of this chapter is that low-revenue clubs can be successful by depending less on free agents and more on developing players out of their own farm system.

In his chapter on building a team brand, Gennaro offers a host of broad sweep generalizations and arbitrary weights to make standard, prosaic recommendations common to the marketing literature. One of his more remarkable statements is found on pages 193-194. To wit: “A team that tries to get through a season with a roster filled with fringe players and minor league prospects is testing the patience of its fans and risking its credibility. Even the 56-win Kansas City Royals had proven major leaguers on their 2005 squad. Matt Stairs and Terrence Long, along with their star player Mike Sweeney, complemented a host of youngsters. For all their faults in the 2005 season, the Royals maintained the credibility and trust of their fans by not ridding themselves of Sweeney’s $11 million contract. For the 2006 season, the Royals loaded up on mature talent with Reggie Sanders, Doug Mientkiewicz, Mark Redman, and Mark Grudzielanek, giving hope to the K.C. faithful.” This worthy team won 62 of its 162 games in 2006.

Gennaro’s closing chapter has some gems on the stadium economic impact literature. On page 238, he writes: “The stadium dialogue seems to quickly degenerate into a ‘he said-she said’ by ‘greedy owners’ and ‘ungrateful municipalities’ about who gets the most benefit from a new ballpark and consequently, the appropriate mix of public versus private funding. The two sides seem to argue so vehemently out of self-interest, citing the results of previous parks, selectively choosing the data that fits their points of view, that they neglect to get at the key issue. ‘Do stadiums enhance the local economy?’ may be the wrong question. The right question is ‘Under what conditions can stadiums enhance the local economy?’” He goes on to claim that if a team plays more day games that it will help local commerce more and, therefore, cities should bargain in their lease agreements to have teams play more day games. His discussion here is either disingenuous or completely ignorant of the academic literature on the subject of economic impact.

In the end, Gennaro’s monograph misses its mark. His treatment of baseball’s economic system offers little of academic value, general reader interest, or team management assistance.

J.C. Bradbury’s The Baseball Economist is a collection of wide-ranging essays on different elements of the game that the author believes are amenable to economic or statistical analysis. The quality of these essays is sharply uneven, with the stronger contributions related to evaluating on-field performance. His topics range from why there are no left-handed catchers, to valuing the worth of a pitching coach, whether having a strong on-deck batter actually helps the current batter or not, why there are more hit batsmen in the American League, a game theory treatment of the game’s steroid problem, assessing the role of entrepreneurial behavior in the front office, an evaluation of the competitive balance issue, an introduction to sabermetrics, how much a ballplayer is worth, and whether MLB is a monopoly. Below I consider some of the collection’s high points and low points. The latter, unfortunately, are more plentiful.

My favorite Bradbury entry convincingly attacks a longstanding baseball myth -- a strong on-deck batter helps the current batter. Bradbury uses data from 1984-1992 to test this relationship and what he comes up with is the following: for every 100 points higher is the OPS (on-base percentage plus slugging percentage of the current batter) of the on-deck batter, the current batter will walk 2.6 percent less, will have a 1.1 percent lower batting average and will hit 3.0 percent fewer home runs. He controls for the OPS of the current batter, the game situation, the ballpark and other factors. Hence, Bradbury concludes that a strong on-deck batter does create an incentive for the pitcher not to walk the current batter, but it also encourages the pitcher to add focus and make tougher pitches in the strike zone, thereby lowering the current hitter’s average and power. While these relationships are statistically significant, their actual impact is very small. His conclusion appears solid and one wonders how long it will take before Joe Buck, Tim McCarver, Jon Miller, et al. catch on.

Bradbury’s chapter on whether it pays for a manager to argue with the umpire is provocative, but unsatisfying. He describes the phenomenon of a manager protesting a call as rent-seeking behavior. The manager attempts to bully the ump, so that the ump will remember the unpleasant experience and will think twice before making another close call against the manager’s team. Bradbury suggests that sometimes the managers succeed in this endeavor, though the statistical evidence he presents is too weak to support his claim. It is rent seeking because there is no net gain, no output increase, just a transfer of marginal calls from one team to another. Meanwhile, the fans, according to Bradbury, have their utility lowered because they have to spend a few extra minutes at the game due to these fits of managerial distemper. Well maybe, but it is also possible that the fans enjoy managerial protests both because they are amusing and because it vicariously vents their own frustration at bad umpire calls. As for a few extra minutes at the ballpark – hey, it’s baseball.

In another interesting essay, Bradbury assembles evidence that Leo Mazzone is actually a pitching coach who makes a positive difference. Bradbury compares pitchers performance under Mazzone with their performance before and after working with him. The evidence appears to support superior skills for Mazzone. Bradbury also explains Mazzone’s philosophy and method. Mazzone has now been pitching coach for the Baltimore Orioles for two years. Perhaps it is time for corroboratory evidence.

From here the book goes downhill. In one chapter Bradbury discusses the presumed advantage that big city teams have. He concludes that (p. 80): “the advantage appears to be slight and virtually meaningless.” His argument here is sloppy. Bradbury’s simple regression finds that variance in city size accounts for 40 percent of the variance in win percentage over a period of years. This seems to indicate a rather substantial impact of city size. Further, the author fails to consider the interactive effect of city size and a team owning its own regional sports channel (RSN), the number of large corporations in the market, or the size of MLB’s assigned team television market – three factors that would have reinforced the effect of city size. Along the way, Bradbury misapprehends the functioning of the amateur draft and overlooks the unequalizing effect of the posting system with Japanese baseball.

In his chapter on what makes for an effective front office, Bradbury singles out two desiderata: having a good team on the field and having a low payroll. Of course, all teams would like that combination, but no team can win every year on a modest payroll. A franchise is a business and there are more factors behind whether or not it will be a successful organization, including effective promotional efforts, good relations with and involvement in the host community, charitable activities, new investments, and profitability, among others. Bradbury then attempts to quantify team rankings by adding up the value produced by all the players on each team and subtracting team payroll, yielding his “net value of team play.” Every team has a positive net value except his lowest ranking team, the Yankees with a negative net value of $29.8 million during 2003-05. This anomalous result comes from the wrongheaded methodology he uses to estimate player marginal revenue product (to be discussed below) and from the narrow definition he adopts to define team success.

His chapter on steroids in baseball employs game theory to model the choice that a player makes whether or not to indulge. He argues that when every player chooses to use steroids it is a Nash equilibrium. This result, however, appears to depend on his arbitrarily chosen values for the supposed productivity gain and the health costs (only $500,000) from indulgence. Bradbury’s analysis ignores the enormous uncertainty that surrounds this choice for players.

Another chapter, “Scouts and Stat-Heads,” provides a generally useful introduction to sabermetric analysis, but Bradbury gets a bit starry-eyed over the presumed power of sabermetrics. On page 147, for instance, Bradbury writes: “Old ways and old scouting methods may disappear, but the end result is a good one for the fan: better and cheaper baseball.” No team is contemplating the elimination of traditional scouting methods, nor is one likely to in the future. New statistical methods have been employed to supplement, not supplant, traditional scouting.

Bradbury’s essay “How to Judge a Hitter or a Pitcher” also overplays the sabermetric hand. Baseball analysts frequently refer to a statistic called hitting with “runners in scoring position” (RISP). It is meant to represent how effective a clutch hitter a player is. Bradbury says folderol: “The problem is that hitting with RISP is not a skill … but a statistical anomaly.” (p. 155) “If hitting with RISP is something a hitter can purposely alter, I have a hard time believing he is holding something back in non-RISP situations” (p. 156). There you have it – there is no such thing as clutch hitting. This is an awfully linear, materialist view of the world where a player’s emotions and his state of physical depletion over a 162-game season play no role. Further, Bradbury is being inconsistent. In his chapter about the on-deck batter, he asserted that a pitcher can ramp it up and pitch more carefully and effectively to the current batter when a strong batter is on deck. So, in Bradbury’s world, pitchers can focus and pitch in the clutch, but hitters can’t turn the same trick. Later in the chapter, Bradbury endorses the proposition from Moneyball that on-base percentage (OBP) is three times as important as slugging percentage (SLG). He arrives at this outcome by running a multiple regression of runs on batting average, OBP and SLG. The coefficient on OBP is almost three times that on SLG. The problem here is not only that the arguments are collinear and the coefficients are less reliable, but that SLG (it counts a homerun as four hits, a triple as three, etc.) is a much higher number than OBP. The coefficient, therefore, will necessarily be smaller on SLG. If elasticity is used instead of the estimated coefficient, OBP is 1.8 times greater than SLG.

Bradbury also discusses the assessment of pitching skills in this chapter. The main argument here is that a pitcher’s ERA from one year to the next is highly variable, but that a pitcher’s walks, strikes and home runs allowed are more stable over time. The inference is that ERA depends more on outside factors, such as a team’s fielding prowess, and, hence, is a poor measure of the inherent skills of a pitcher. While there is something compelling to this logic, it seems caution is in order. First, a pitcher’s skills may actually vary from year to year, along with his ERA, as other factors change, such as, his ballpark, his pitching coach, his bullpen, his team’s offense, the angle of his arm slot, his confidence level, etc. This variability does not mean that the skill is spurious. Second, if all we consider is strikeouts, walks and home runs, what are we saying about sinkerball pitchers who induce groundballs or pitchers who throw fastballs with movement or offspeed pitches that induce weak swings and popups? Didn’t Bradbury already write that with a strong on-deck batter, pitchers can pitch more effectively within the strike zone?

Next, Bradbury offers a chapter on the worth of a ballplayer. He gets off to a bad start here by misrepresenting the functioning of the players’ market and the terms of the collective bargaining agreement. He then misspecifies his team revenue function, leaving out RSN ownership, the number of large corporations in the host market, the size of the team’s assigned television territory, among other factors. But the fatal problem is that Bradbury’s methodology unwittingly identifies a player’s average revenue product, not his marginal revenue product. By his reckoning, all of a team’s revenue is attributed to the players, leaving nothing left over for front offices expenses, stadium expenses, minor league operations, or profits. Given this misstep, it is not surprising that Bradbury finds players at all levels (under reserve, arbitration eligible and free agents) are paid less than what he estimates they are worth.

Bradbury then moves on to the baseball product market, asking “Is MLB a Monopoly?” Bucking all scholarly analysis and legal decisions on the question, Bradbury writes (p. 201): “I’m not sure MLB is a monopoly.” Then, in a comedy of errors, he explains his ambivalence. He writes that Judge Kenesaw Mountain Landis’ decision that baseball was not interstate commerce gave the game its antitrust exemption and that (p. 203) “the Supreme Court has upheld the Landis decision on several occasions.” Here Bradbury is confusing two cases. The first was a suit brought by the owners of the Federal League teams in January 1915 against baseball’s reserve clause. This case went before Judge Landis. Landis, however, never issued a decision. The parties settled at the end of the year. The second was a litigation brought by the owners of the Baltimore Terrapins of the Federal League because they did not believe that the terms of the settlement were fair to their franchise. After losing in district court (where Landis played no role), baseball appealed the decision and won. The Terrapins then appealed before the Supreme Court, where the case was heard in April 1922. A few months later the Supreme Court decided in baseball’s favor and the antitrust exemption was born.

Bradbury then distorts the record further by asserting (p. 205): “At the heart of the argument that MLB acts like a monopolist is the existence of the antitrust exemption.” He cites no sources for this claim, because there are none. Each team sport league is a monopolist because it is the sole producer of its product and has no close substitutes. The NFL has no blanket exemption and it is a monopoly; likewise the NBA. Bradbury then writes referring to the NFL, NBA, NHL and MLB that “each of these enjoys some antitrust exemptions for collective bargaining with labor unions ….” Here, of course, it is not an exemption granted to the leagues, but a general statutory exemption granted to all labor unions by the Clayton Act of 1914. Similarly, the non-statutory exemption --which enables a union to surrender certain labor market rights in exchange for other benefits in arms’ length bargaining -- applies generally to all U.S. industries. Bradbury continues (p. 208): “There is no strong evidence that the antitrust exemption provides any monopoly privileges to MLB other than protecting it from expensive lawsuits.” While the value of baseball’s exemption today is not what it used to be, there is still a good case to be made that MLB’s minor leagues and perhaps its amateur draft could not exist in their present form were it not for the exemption. (This matter is actually rather complicated because any of these arrangements can be subjected to a rule of reason interpretation, balancing their pro- and anti-competitive effects.)

Bradbury’s last essay argues that the market for top-level professional baseball in the United States is contestable. If this were true, then the earlier question about whether or not MLB is a monopoly might be moot. Here Bradbury makes two points. First, if there is an aspect of the industry that is not a natural monopoly and, hence, constitutes an artificial barrier to entry, it is the subsidies from local governments that teams receive for the construction of their stadiums. But, he avers, this is not really an issue because (p. 220) “the public does not seem averse to subsidizing major sports teams from leagues other than the dominant existing league.” It is clear that Bradbury has never been involved in starting a new or non-dominant league. His notion that politicians are not averse to providing subsidies to teams from these upstart leagues is just plain wrong. Second, Bradbury goes on to argue that MLB’s market is contestable. He does this by discussing the emergence of the American Association in 1882 and the American League in 1901. He further adduces what he erroneously calls the “Central League” (real name: the Continental League) forcing baseball to expand the number of its teams in 1961. Leaving details aside, the difficulty with Bradbury’s claim is that the industry’s economic structure today is very different from what it was 57 or 120 years ago.

Bradbury, then, whiffs in his effort to expand his analysis beyond the narrow confines of the baseball diamond. After a promising beginning, The Baseball Economist fails in its intent to expose the real game.